**ERIC Number:**EJ1217292

**Record Type:**Journal

**Publication Date:**2019-Apr

**Pages:**6

**Abstractor:**ERIC

**ISBN:**N/A

**ISSN:**ISSN-0025-5769

**EISSN:**N/A

A Riddle: Probabilities and p-Values

CadwalladerOlsker, Todd

Mathematics Teacher, v112 n6 p462-467 Apr 2019

Students studying statistics often misunderstand what statistics represent. Some of the most well-known misunderstandings of statistics revolve around null hypothesis significance testing. One pervasive misunderstanding is that the calculated p-value represents the probability that the null hypothesis is true, and that if p < 0.05, there is less than a 5 percent chance that the null hypothesis is true (Nickerson 2000). To help students understand what the p-value in null hypothesis significance testing really means, the author use the following riddle from a book evocatively titled "The Book of Sense and Nonsense Puzzles" (Shushan 1985, p. 33): "You throw a die 20 times, and it comes up 5 on 17 out of 20 tosses. What's your best bet for the next roll?" This riddle is an opportunity to stimulate students' curiosity. After all, if the die is probably loaded, a natural follow-up question is "What is the probability that the die is loaded?" This question is surprisingly tricky. In fact, the author asks his students to set this question aside at first, and instead ask, "What is the probability that a fair die would come up 5 on 17 of 20 tosses?" This is the question answered by p-values in null hypothesis significance testing.

Descriptors: Statistics, Mathematics Education, Misconceptions, Hypothesis Testing, Computation, Probability, Mathematics Instruction, Teaching Methods, Bayesian Statistics

National Council of Teachers of Mathematics. 1906 Association Drive, Reston, VA 20191. Tel: 800-235-7566; Tel: 703-620-9840; Fax: 703-476-2570; e-mail: NCTM@nctm.org; Web site: http://www.nctm.org/publications/mathematics-teacher/

**Publication Type:**Journal Articles; Reports - Descriptive

**Education Level:**N/A

**Audience:**N/A

**Language:**English

**Sponsor:**N/A

**Authoring Institution:**N/A

**Grant or Contract Numbers:**N/A